Put the raisins and marsala in a small saucepan and heat until hot but not boiling. Pour into a bowl and leave to stand for 2 hours until the raisins have plumped up.
Place 16 mini silicone muffin cases on a baking sheet.
Mix the coffee powder with the measurement water. Sift the flour and baking powder into a bowl. Stir in the sugar.
Mix together the yogurt, egg, oil and coffee mixture and stir in the raisins and any unabsorbed liquid. Add to the dry ingredients. Using a large metal spoon, stir the ingredients together until only just combined. Divide among the cases.
Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for about 12 minutes until risen and firm. Leave in the cases for 2 minutes, then transfer to a wire rack to cool.
Make the icing by mixing the espresso coffee powder in a small bowl with the hot water until blended. Beat in the icing sugar and drizzle over the muffins.